Obtaining the natural frequencies of linear time-invariant dynamic systems from driving-point system-function measurements employing conceptual source-measure units

I. R. Rao, K. Shubhanga
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Abstract

This paper presents two mathematical conceptualizations of driving-point system-function measurement of linear time-invariant (LTI) systems with lumped-parameter description. Whereas the formalization of this dual pair of Source-Measure Units (SMU) has been - for the twin purposes of ease of demonstration and ready cognizance - effected with a specific relevance to electrical quantities, the underlying concept of system-function is sufficiently general to be universally applicable to all classes of LTI systems. The formulation has been done in the time-domain, thus retaining full immediacy with the real system variables. The outcome of the measurement, therefore, upon due rationalization, emerges as a rationic polynomial. The natural frequencies of the system are then extractible from the characteristic polynomial, which latter is contained in the measured rationic. The `naturality' of the system-under-test as observed from a specified port-of-access is thus laid bare. The method is illustrated through examples, which also show the invariance of the system characteristic polynomial with respect to the point of view of the observer, except in cases of pole-zero cancellation. An alternative interpretation of the singularities of the system-function has also been furnished.
利用概念源测单位从驱动点系统函数测量中获得线性时不变动力系统的固有频率
本文提出了线性时不变系统驱动点系统功能测量的两个数学概念,并给出了集总参数描述。然而,由于易于演示和易于识别的双重目的,这种双源测量单元(SMU)的形式化已经与电量的特定相关性产生了影响,系统函数的潜在概念足够普遍,可以普遍适用于所有类别的LTI系统。该公式是在时域内完成的,因此与实际系统变量保持完全的即时性。测量的结果,因此,在适当的合理化,出现为一个有理多项式。然后从特征多项式中提取系统的固有频率,特征多项式包含在被测有理域中。因此,从指定的访问端口观察到的被测系统的“自然性”就暴露无遗了。通过实例说明了该方法,该方法还证明了系统特征多项式相对于观测者的观点的不变性,除了极点-零抵消的情况。还提供了对系统函数奇异性的另一种解释。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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